Since your design approaches RF/Microwave frequencies, I think it is easier to
understand the impact of vias on the differential pairs from the concept of
matched impedance.

Differential pairs is basically two conductors running in parallel. There are
two fundamental modes that propagate on the line. One is the odd mode
(differential mode), and the other is the even mode (common mode).
Both modes have the same propgation constants. But odd and even mode has
different impedances. The important thing to remember is that both modes
can exist on the structure at the SAME time. One can control which mode may
exist through proper excitation. In differential pair case, one simply drives the
structure with a pair of differential drivers. When discontinuities such as vias
or bends are introduced, the structure is no longer perfectly matched. Higher order
modes (including the even (or common) mode) are introduced. The higher the
frequency, the more impact of discontinuities. In order to make sure the
diffential pairs work as desired, one need to match the odd (differential) mode
impedance.

As you suggested, one could find out the amount of impact of vias by including
an equivalent circuit model obtained by using an 3D simulator. However, do not expect
this as a simple push of buttons.